Concept

Binary tree

Related publications (32)

From trees to barcodes and back again II: Combinatorial and probabilistic aspects of a topological inverse problem

Kathryn Hess Bellwald, Lida Kanari, Adélie Eliane Garin

In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general position, based ...

2024

Succinct ordering and aggregation constraints in algebraic array theories

Viktor Kuncak, Rodrigo Raya

We discuss two extensions to a recently introduced theory of arrays, which are based on considerations coming from the model theory of power structures. First, we discuss how the ordering relation on the index set can be expressed succinctly by referring t ...

Elsevier Science Inc2024

On Speed and Advantage : Results in Information Velocity and Monitoring Problems

Reka Inovan

Information theory has allowed us to determine the fundamental limit of various communication and algorithmic problems, e.g., the channel coding problem, the compression problem, and the hypothesis testing problem. In this work, we revisit the assumptions ...

EPFL2024

Field Guide to Northern Tree-related Microhabitats: Descriptions and size limits for their inventory in boreal and hemiboreal forests of Europe and North America

Rita Bütler Sauvain

A tree-related microhabitat (abbreviated as TreM) is a morphological feature present on a tree, which is used by sometimes highly specialised species during at least one part of their life cycle. These features may serve as shelters, breeding spots, or cru ...

Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Switzerland2024

Fairness and Explainability in Clustering Problems

Xinrui Jia

In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...

EPFL2023

Fundamental Limits in Statistical Learning Problems: Block Models and Neural Networks

Elisabetta Cornacchia

This thesis focuses on two selected learning problems: 1) statistical inference on graphs models, and, 2) gradient descent on neural networks, with the common objective of defining and analysing the measures that characterize the fundamental limits.In the ...

EPFL2023

From Trees to Barcodes and Back Again:A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B involve ...

EPFL2022

Genomic and metabolic adaptations of biofilms to ecological windows of opportunity in glacier-fed streams

Tom Ian Battin, Hannes Markus Peter, Susheel Bhanu Busi, Grégoire Marie Octave Edouard Michoud, Leïla Ezzat, Massimo Bourquin, Matteo Tolosano, Tyler Joe Kohler, Stylianos Fodelianakis, Paraskevi Pramateftaki, Vincent Henri De Staercke, Michail Styllas, Martina Andrea Schön

In glacier-fed streams, ecological windows of opportunity allow complex microbial biofilms to develop and transiently form the basis of the food web, thereby controlling key ecosystem processes. Using metagenome-assembled genomes, we unravel strategies tha ...

Springer2022

Key factors determining the presence of Tree-related Microhabitats: A synthesis of potential factors at site, stand and tree scales, with perspectives for further research

Tree-related microhabitats (TreMs) have been identified as key features for forest-dwelling taxa and are often employed as measures for biodiversity conservation in integrative forest management. However, managing forests to ensure an uninterrupted resourc ...

2022

Abstractions for Type-Level Programming

Olivier Eric Paul Blanvillain

Over the past decade, the Scala community has shown great interest in using type-level programming to obtain additional type safety.Unfortunately, the lack of support from the Scala compiler has been a barrier to the adoption of that technique, notably due ...

EPFL2022

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